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Grimmett and McDiarmid suggested a simple heuristic for finding stable sets in random graphs. They showed that the heuristic finds a stable set of size $simlog_2 n$ (with high probability) on a $G(n, 1/2)$ random graph. We determine the asymptotic distribution of the size of the stable set found by the algorithm.
We consider the {em vector partition problem}, where $n$ agents, each with a $d$-dimensional attribute vector, are to be partitioned into $p$ parts so as to minimize cost which is a given function on the sums of attribute vectors in each part. The pr
Minimizing the discrepancy of a set system is a fundamental problem in combinatorics. One of the cornerstones in this area is the celebrated six standard deviations result of Spencer (AMS 1985): In any system of n sets in a universe of size n, there
We develop an approximation algorithm for the partition function of the ferromagnetic Potts model on graphs with a small-set expansion condition, and as a step in the argument we give a graph partitioning algorithm with expansion and minimum degree c
It is known that testing isomorphism of chordal graphs is as hard as the general graph isomorphism problem. Every chordal graph can be represented as the intersection graph of some subtrees of a tree. The leafage of a chordal graph, is defined to be
For every constant $d geq 3$ and $epsilon > 0$, we give a deterministic $mathrm{poly}(n)$-time algorithm that outputs a $d$-regular graph on $Theta(n)$ vertices that is $epsilon$-near-Ramanujan; i.e., its eigenvalues are bounded in magnitude by $2sqr